Mathematics concepts are developed through children's active involvement with their environment. Key concepts include one-to-one correspondence, classification, patterns, functions, geometry, measurement, data analysis and probability. These concepts are fostered through hands-on learning with manipulatives, games, activities in other subjects like science and art, and exploration outdoors. Careful observation and assessment of each child's mathematical development is important for planning effective instruction.

1. Chapter 5Math

2. MathematicsIs everywhereDaily living provides a math-rich environmentMath must be hands-on and DAPRelationships and repetition are key to math learning

3. Concept DevelopmentConcepts are the building blocks of knowledgeConcepts are acquired through children’s active involvement with their environmentConcepts are fostered by solving problems

4. Names Associated with Mathematical ConceptsPiagetTwo types of knowledgePhysicalLogico-MathematicalVygotskySkills learned from those who have more skillsZone of proximal developmentGardnerLogical-Mathematical intelligence

5. Math Language DevelopmentMath language development occurs as children develop number sense and logical ways of thinking about time, space, and other mathematical ideasLanguage based on recommendations from NCTM’s Principles and Standards

6. Math ConceptsOne-to-one correspondenceEach object has the value of oneClassifying and sortingGrouping objects by a common characteristic—size, shape, or colorPatterns, functions, and algebraSequence of numbers, colors, objects, sounds, shapes, or movements that repeat, in the same order, over and overSeriation

7. Math Concepts (continued)Geometry and spatial senseChildren’s awareness of themselves in relation to the people and objects around themMeasurementData analysis and probabilityProblem solving

8. Math ExperiencesGamesFolder gamesLotto gamesBingoMatching outdoor activitiesCountingClimbingFinding shapesComparing

9. Math across the CurriculumScienceSorting collectionsGraphingChartingCountingCookingMeasuringCountingArtOutliningLanguage, literacy, and literatureSpeakingReading

10. ManipulativesCreate a manipulative centerThink about the purpose and objectivesThe teacher’s roleCriteria for selecting materials, including multicultural and needs of identified childrenManipulative toys, games, and materialsSelf-correcting, structured toysOpen-ended toys

11. Materials for Developing Math ConceptsChildren will naturally explore their environmentsRole of teacher to provide words, materials, and resources to scaffold learningMaterials could includeBalancesBingo cardsCalculatorsGeoboardsMagnetic boardsObjects to count, sort, classify, make patternsTable gamesTable blocks

12. Technology and MathematicsCalculators should be available for use by young childrenTeachers should review software carefullyOpen-ended software preferred

13. Observation, Assessment, and EvaluationAssessment is crucial to effective teachingCareful assessment can help you when planning for culturally and linguistically diverse childrenAnecdotal assessment form helpfulKeep anecdotal records on all children

14. Encouraging Family SupportInform them about opportunities for math at homeSorting laundryBy colorBy shapeBy family membersSetting the table

15. Tips for TeachersEncourage exploration by childrenFocus on process, not “correct” answerDiscover togetherUseNumber songs and booksRhymes and rhythmPlan appropriate activities